New progress in the cobalt-catalysed synthesis of aromatic organozinc compounds by reduction of aromatic halides by zinc dust

The experimental conditions of the cobalt-catalysed synthesis of aromatic organozinc species from the corresponding bromides have been optimised. The preparation of numerous aromatic organozinc reagents under these optimised conditions is reported, with yields between 67 and 99%.     

Asymptotic Poisson Character of Extremes in Non-Stationary Gaussian Models

Let X be a non-stationary Gaussian process, asymptotically centered with constant variance. Let u be a positive real. Define R_u(t) as the number of upcrossings of level u by the process X on the interval (0, t]. Under some conditions we prove that the sequence of point processes (R_u)_u>0 converges weakly, after normalization, to a standard Poisson process as u tends to infinity. In consequence of this study we obtain the weak convergence of the normalized supremum to a Gumbel distribution.AMS 2000 Subject Classifications Primary—60G70, 60G15     

An ordinal sorting method for group decision-making

Several group decision-making methods were proposed with the aim to establish, from individual opinions, a collective one. However, the literature review of such methods show that, until now, few of them accept individual preferences expressed in partial pre-orders or, more generally, in preferences relational systems (p.r.s.). In addition, the majority of these methods produce a ranking on the alternative set, i.e. they concern the ranking decision-making problematic. In fact, the efforts provided to develop methods which treat, for example, the sorting problematic, remain insufficient. For these reasons, we propose in this paper an ordinal sorting method which determines, from individual p.r.s., at least one collective assignment which takes into account the relative importance of the members. If there is more than one collective assignment, an interactive procedure to reach a consensus assignment is proposed.     

Numerical simulations of gas-particle flows with combustion

This work is devoted to the numerical modelling of a reactive gas-particle flow that arises in internal ballistic. The model, proposed by Gough [2], takes into account complex physical phenomena such as mass transfer, drag force or intra granular stress. A non-conservative finite volume approach adapted from [11] is applied in order to simulate the model. After an academic validation test case of the scheme, the combustion propagation ignited by a cylindrical perforated primer is then simulated and compared with experiments.     

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Algebraic Topology for Minimal Cantor Sets

It will be shown that every minimal Cantor set can be obtained as a projective limit of directed graphs. This allows to study minimal Cantor sets by algebraic topological means. In particular, homology, homotopy and cohomology are related to the dynamics of minimal Cantor sets. These techniques allow to explicitly illustrate the variety of dynamical behavior possible in minimal Cantor sets. submitted 20/07/05, accepted 18/10/05     

Global existence of small solutions for quadratic quasilinear Klein-Gordon systems in two space dimensions

Consider a quasi-linear system of two Klein-Gordon equations with masses m₁, m₂. We prove that when m₁≠2m₂ and m₂≠2m₁, such a system has global solutions for small, smooth, compactly supported Cauchy data. This extends a result proved by Sunagawa (J. Differential Equations 192 (2) (2003) 308) in the semi-linear case. Moreover, we show that global existence holds true also when m₁=2m₂ and a convenient null condition is satisfied by the nonlinearities.     

Nielsen-Thurston reducibility and renormalization

Consider an orientation preserving homeomorphism of the 2-disk with an infinite set of nested periodic orbits , such that, for all , the restriction of to the complement of the first orbits, from to , is times reducible in the sense of Nielsen and Thurston. We define combinatorial renormalization operators for such maps, and study the fixed points of these operators. We also recall the corresponding theory for endomorphisms of the interval, and give elements of comparison of the theories in one and two dimensions.